# Beer'Lamberts Law

## Homework Statement

I am trying to understand a formula on a paper. On page 3138-3139 they express the Beer-Lamberts law in which they replace the concentration n with an equation involving the volume ratio ( I am guessing its the molarfraction of the investigated species). What I would like to know is the unit of Boltzmann constant kb to make this happen. I don't see how the units can fit.

## Homework Equations

$$\frac{cp}{kT}$$

where c is the volume part (volume ratio) of the absorbing gas in the gas mixture, T is the temperature of the gas, k is the boltzmann constant (unit???), p is pressure in [atm].

## The Attempt at a Solution

This equation should fit to Beer law,

exp( - alpha(v)*n*l ) = exp (- tau )

where tau is unitless and alpha(v) is specific absorption coefficient per
absorbing particle and is caluclated with help of Hitran by alpha(v) = S(T)*g(v-vo) [ unit: 1/(molecule cm-2) ] and l is path length of radiation through the absorbing medium [ unit: cm ].

It's the unit of n I am trying to determine, and thus boltzmann constant.

According to above it should be [molecules cm-3] so that tau becomes unitless.

What I know the unit if Kb is 0.659 cm-1 K-1. And there is the [ atm ] from the pressure I am missing and [ molecules ]. If c is a fraction this is unitless, so I don't see how this can go together.

This has been taken from this paper: http://iopscience.iop.org.ludwig.lub.lu.se/0022-3727/35/23/315/pdf/0022-3727_35_23_315.pdf

"Experimental verification of gas spectra calculated for high temperatures using the
HITRAN/HITEMP database"

My goal is to plot the transmission as function of % of the species.

Last edited:

Borek
Mentor
You are aware of the fact that paper you linked to is available only to those that can log in?

You are aware of the fact that paper you linked to is available only to those that can log in?

Well, yes. That is why I have written everything in detail. However if you have access to the university as student or teacher you should be able to log in and read it.

I noticed that the unit is [ cm -2 atm -1 ] for the linestrength S. In hitran this is [ cm-1 / ( molecules cm-2 ) ] and absorption coefficent is [ cm-1].

I don't see the connection.